Energetics of lateral eddy diffusion/advection: Part IV. Energetics of diffusion/advection in sigma coordinates and other coordinates

Gravitational potential energy （GPE） source and sink due to stirring and cabbeling associated with sigma dif fusion/ advection is analyzed. It is shown that GPE source and sink is too big, and they are not closely linked to physical property distribution, such as temperature, salinity and velocity. Although the most frequently quoted advantage of sigma coordinate models are their capability of dealing with topography; the exces sive amount of GPE source and sink due to stirring and cabbeling associated with sigma diffusion/advec tion diagnosed from our analysis raises a very serious question whether the way lateral diffusion/advection simulated in the sigma coordinates model is physically acceptable. GPE source and sink in three coordinates is dramatically different in their magnitude and patterns. Overall, in terms of simulating lateral eddy diffu sion and advection isopycnal coordinates is the best choice and sigma coordinates is the worst. The physical reason of the excessive GPE source and sink in sigma coordinates is further explored in details. However, even in the isopycnal coordinates, simulation based on the Eulerian coordinates can be contaminated by the numerical errors associated with the advection terms.

Energetics of lateral eddy diffusion/advection: Part I. Thermodynamics and energetics of vertical eddy diffusion

Two important nonlinear properties of seawater thermodynamics linked to changes of water density, cab beling and elasticity （compressibility）, are discussed. Eddy diffusion and advection lead to changes in den sity; as a result, gravitational potential energy of the system is changed. Therefore, cabbeling and elasticity play key roles in the energetics of lateral eddy diffusion and advection. Vertical eddy diffusion is one of the key elements in the mechanical energy balance of the global oceans. Vertical eddy diffusion can be con ceptually separated into two steps： stirring and subscale diffusion. Vertical eddy stirring pushes cold/dense water upward and warm/light water downward; thus, gravitational potential energy is increased. During the second steps, water masses from different places mix through subscale diffusion, and water density is increased due to cabbeling. UsingWOA01 climatology and assuming the vertical eddy diffusivity is equal to a constant value of 2x103 pa2/s, the total amount of gravitational potential energy increase due to vertical stirring in the world oceans is estimated at 263 GW. Cabbeling associated with vertical subscale diffusion is a sink of gravitational potential energy, and the total value of energy lost is estimated at 73 GW. Therefore, the net source of gravitational potential energy due to vertical eddy diffusion for the world oceans is estimated at 189 GW.

Energetics of lateral eddy diffusion/advection: Part III. Energetics of horizontal and isopycnal diffusion/ advection

Gravitational Potential Energy （GPE） change due to horizontal/isopycnal eddy diffusion and advection is examined. Horizontal/isopycnal eddy diffusion is conceptually separated into two steps： stirring and sub scale diffusion. GPE changes associated with these two steps are analyzed. In addition, GPE changes due to stirring and subscale diffusion associated with horizontal/isopycnal advection in the Eulerian coordinates are analyzed. These formulae are applied to the SODA data for the world oceans. Our analysis indicates that horizontal/isopycnal advection in Eulerian coordinates can introduce large artificial diffusion in the model. It is shown that GPE source/sink in isopycnal coordinates is closely linked to physical property distribution, such as temperature, salinity and velocity. In comparison with z-coordinates, GPE source/sink due to stir ring/cabbeling associated with isopycnal diffusion/advection is much smaller. Although isopycnal coordi nates may be a better choice in terms of handling lateral diffusion, advection terms in the traditional Eule rian coordinates can produce artificial source of GPE due to cabbeling associated with advection. Reducing such numerical errors remains a grand challenge.

A modified method to estimate eddy diffusivity in the North Pacific using altimeter eddy statistics

The method proposed by Stammer (1998) is modified using eddy statistics from altimeter observation to obtain more realistic eddy diffusivity (K) for the North Pacific. Compared with original estimates, the modified K has remarkably reduced values in the Kuroshio Extension (KE) and North Equatorial Counter Current (NECC) regions, but slightly enhanced values in the Subtropical Counter Current (STCC) region. In strong eastward flow areas like the KE and NECC, owing to a large difference between mean flow velocity and propagation velocity of mesoscale eddies, tracers inside the mesoscale eddies are transported outside rapidly by advection, and mixing length L is hence strongly suppressed. The low eddy probability (P) is also responsible for the reduced K in the NECC area. In the STCC region, however, L is mildly suppressed and P is very high, so K there is enhanced. The zonally-averaged K has two peaks with comparable magnitudes, in the latitude bands of the STCC and KE. In the core of KE, because of the reduced values of P and L, the zonally-averaged K is a minimum. Zonally-integrated eddy heat transport in the KE band, calculated based on the modified K, is much closer to the results of previous independent research, indicating the robustness of our modified K. The map of modified K provides useful information for modeling studies in the North Pacific.

Influence of Vertical Eddy Diffusivity Parameterization on Daily and Monthly Mean Concentrations of O3 and NOy

Two parameterization schemes for vertical eddy diffusivity were utilized to investigate their impacts on both the daily and monthly mean concentrations of ozone and NOy, which are the major fractions of the sum of all reactive nitrogen species, i.e., NOy=NO＋NO2＋HNO3＋PAN. Simulations indicate that great changes in the vertical diffusivity usually occur within the planetary boundary layer （PBL）. Daily and monthly mean concentrations of NOy are much more sensitive to changes in the vertical diffusivity than those of ozone and ozone and NOy levels only at or in （relatively） clean sites and areas, where long-range transport plays a crucial role, display roughly equivalent sensitivity. The results strongly suggest that a widely-accepted parameterization scheme be selected and the refinement of the model＇s vertical resolution in the PBL be required, even for regional and long-term studies, and ozone only being examined in an effort to judge the model＇s performance be unreliable, and NOy be included for model evaluations.

Eddy diffusivity and coherent mesoscale eddy analysis in the Southern Ocean

The spatial distribution of eddy diffusivity,basic characteristics of coherent mesoscale eddies and their relationship are analyzed from numerical model outputs in the Southern Ocean.Mesoscale fluctuation information is obtained by a temporal-spatial filtering method,and the eddy diffusivity is calculated using a linear regression analysis between isoneutral thickness flux and large-scale isoneutral thickness gradient.The eddy diffusivity is on the order of O(103 m2/s)with a significant spatial variation,and it is larger in the area with strong coherent mesoscale eddy activity.The mesoscale eddies are mainly located in the upper ocean layer,with the average intensity no larger than 0.2.The mean radius of the coherent mesoscale cyclonic(anticyclonic)eddy gradually decays from(121.2±10.4)km((117.8±9.6)km)at 30°S to(43.9±5.3)km((44.7±4.9)km)at 65°S.Their vertical penetration depths(lifespans)are deeper(longer)between the northern side of the Subpolar Antarctic Front and 48°S.The normalized eddy diffusivity and coherent mesoscale eddy activity show a significant positive correlation,indicating that coherent mesoscale eddy plays an important role in eddy diffusivity.

^(226)Ra and ^(228)Ra tracer study on nutrient transport in east coastal waters of Hainan Island,China

Material fluxes （e.g., nutrients） from coastal waters to offshore areas play an important role in controlling the water quality of the adjacent sea areas not only by increasing nutrient concentration hut also by changing nutrient structures. In this study, naturally occurring isotopes, ^226Ra and ^228Ra, were measured with the alpha spectrometry in the Wenjiao-Wenchang and Wanquan estuaries and adjacent sea areas along the east coast of Hainan Island. The excess ^226Ra and ^228Ra activities were observed by comparison with the values derived from the conservative mixing of freshwater and seawater end-members in both estuaries. Using a one-dimensional diffusion model, the horizontal eddy diffusion coefficient of 3.1 6 × 10^5 cm^2/s, for nutrients diffusing from their sources, was derived from 228Ra activities. Consequently, the corresponding nutrient fluxes flowing into the coastal waters were assessed. The results can provide useful information for the study of the mixing and exchange processes of coastal waters as well as dissoluble pollutant transport in this sea area.

Radium-traced nutrient outwelling from the Subei Shoal to the Yellow Sea:Fluxes and environmental implication

The Subei Shoal is the largest sandy ridge in the southern Yellow Sea and is important source for nutrient loading to the sea.Here,the nutrient fluxes in the Subei Shoal associated with eddy diffusion and submarine groundwater discharge(SGD)were assessed to understand their impacts on the nutrient budget in the Yellow Sea.Based on the analysis of 223 Ra and 224 Ra in the field observation,the offshore eddy diffusivity mixing coefficient and SGD were estimated to be 2.3×10^(8)cm^(2)/s and 2.6×10^(9)m^(3)/d(16 cm/d),respectively,in the Subei Shoal.Combined the significant offshore decreasing gradients of nutrient in seawater of the Subei Shoal,the spatially integrated nutrient outwelling fluxes to the Yellow Sea were 262-1465μmol/(m^(2)·d)for DIN,5.2-21μmol/(m^(2)·d)for DIP and711-913μmol/(m^(2)·d)for DSi.Compared to the riverine input,atmospheric deposition and mariculture,nutrient outwelling from the Subei Shoal might play an important role in nutrient budget of the Yellow Sea.These nutrient fluxes could provide 4.1%-23%N and 1.3%-5.3%P requirements for the primary productivity,and the deviated DIN/DIP ratios have the potential to affect the growth of phytoplankton in the marine ecosystem of the Yellow Sea.

Liquid Axial Mixing in Packed Tower at Elevated Pressure

Liquid phase axial mixing was measured with the tracer technique in a packed column with inner diameter of 0.15m, in which the structured packing, Mellapak 350Y, was installed. Tap water as the liquid phase flowed down through the column and stagnant gas was at elevated pressure ranging from atmospheric to 2.0MPa. The model parameters of Bo and 9 were estimated with the least square method in the time domain. As liquid flow rate was increased, the liquid axial mixing decreased. Under our experimental conditions, the effect of pressure on Bo number on single liquid phase was negligible, and eddy diffusion was believed to be the primary cause of axial mixing in liquid phase.

Mesoscale eddies and their dispersive environmental impacts in the Persian Gulf

As the mesoscale eddies in oceans and semi-enclosed seas are significant in horizontal dispersion of pollutants,we investigate the seasonal variations of these eddies in the Persian Gulf(PG)that are usually generated due to seasonal winds and baroclinic instability.The sea surface height(SSH)data from 2010 to 2014 of AVISO are used to identify and track eddies,using the SSH-based method.Then seasonal horizontal dispersion coefficients are estimated for the PG,using the properties of eddies.The results show an annual mean of 78 eddies with a minimum lifetime of one week.Most of the eddies are predominantly cyclonic(59.1%)and have longer lifetimes and higher diffusion coefficients than the anti-cyclonic eddies.The eddy activity is higher in warm seasons,compared to that of cold seasons.As locations with high eddy diffusion coefficients are high-risk areas by using maps of horizontal eddy diffusion coefficients,perilous times and locations of the release of pollutants are specified to be within the longitude from 51.38°E to 55.28°E.The mentioned areas are located from the Strait of Hormuz towards the northeast of the PG,closer to Iranian coast.Moreover,July can be considered as the most dangerous time of pollution release.

Thermal fronts and cross-frontal heat flux in the southern Huanghai Sea and the East China Sea

Synoptic features in/around thermal fronts and cross-frontal heat fluxes in the southern Huanghai./Yellow Sea and East China Sea （HES） were examined using the data collected from four airborne expendable bathythermograph surveys with horizontal approxmately 35 km and vertical 1 m（from the surface to 400 m deep） spacings. Since the fronts are strongly affected by HES current system, the synoptic thermal features in/around them represent the interaction of currents with surrounding water masses. These features can not be obtained from climatological data. The identified thermal features are listed as follows ： （ 1 ） multiple boundaries of cold water, asymmetric thermocline intrusion, locally-split front by homogeneous water of approxmately 18 ℃, and mergence of the front by the Taiwan Warm Current in/around summertime southern Cheju - Changjiang/Yangtze front and Tsushima front; （2） springtime frontal eddy-like feature around Tsushima front; （3） year-round cyclonic meandering and summertime temperature-inversion at the bottom of the surface mixed layer in Cheju - Tsushima front; and （4） multistructure of Kuroshio front. In the Kuroshio front the mean variance of vertical temperature gradient is an order of degree smaller than that in other HES fronts. The southern Cheju- Changjiang front and Cheju -Tsushima front are connected with each other in the summer with comparable cross-frontal temperature gradient. However, cross-frontal heat flux and lateral eddy diffusivity are stronger in the southern Cheju - Changjiang front. The cross-frontal heat exchange is the largest in the mixing zone between the modified Huanghai Sea bottom cold water and the Tsushima Warm Current, which is attributable to enhanced thermocline intrusions.

The cruise observation of turbulent mixing in the upwelling region east of Hainan Island in the summer of 2012

The turbulent mixing in the upwelling region east of Hainan Island in the South China Sea is analyzed based on in situ microstructure observations made in July 2012. During the observation, strong upwelling appears in the coastal waters, which are 3℃ cooler than the offshore waters and have a salinity 1.0 greater than that of the offshore waters. The magnitude of the dissipation rate of turbulent kinetic energy ε in the upwelling region is O（10–9 W/kg）, which is comparable to the general oceanic dissipation. The inferred eddy diffusivity Kρ is O（10–6 m2/s）, which is one order of magnitude lower than that in the open ocean. The values are elevated to Kρ≈O（10–4 m2/s） near the boundaries. Weak mixing in the upwelling region is consistent with weak instability as a result of moderate shears versus strong stratifications by the joint influence of surface heating and upwelling of cold water.The validity of two fine-scale structure mixing parameterization models are tested by comparison with the observed dissipation rates. The results indicate that the model developed by Mac Kinnon and Gregg in 2003 provides relatively better estimates with magnitudes close to the observations. Mixing parameterization models need to be further improved in the coastal upwelling region.

Local Similarity Relationships of Non-Dimensional Wind and Temperature Gradient in the Tower-Layer Atmosphere over Beijing City

Micrometeorological data for wind and temperature from a 325 m high tower in Beijing City are analyzed by use of local similarity theory. Non-dimensional wind and temperature gradients, Phi(m) and Phi(h), are determined by three techniques called, respectively, eddy-correlation, mean profiles and inertia-subrange cospectra (ISC) method for a wide range of atmospheric stratification from unstable to stable conditions. Average dissipation rate Phi(e) of turbulent kinetic energy (TKE) is evaluated from u-spectrum, as a quantity required in the last technique. Ratio of the eddy transfer coefficients, alpha(= K-h / K-m), is calculated from Phi(m) and Phi(h) estimations. The results from various techniques are compared with each other and with some available empirical results in the tower-layer, It is shown that the empirical relationships determined by mean profiles and ISC methods in the lower-layer turbulence ore in agreement with each other and with some other results.

A MODEL FOR THE SIMULATION OF CROSSWIND INTEGRATED CONCENTRATIONS IN THE SURFACE-BASED INVERSION LAYER

A dispersion model for the estimation of crosswind integrated concentrations in the surface-based inversion is proposed.The generalized forms of eddy diffusivity with spatial dependence in both horizontal and vertical directions and vertical height-dependent wind speed are considered.In view of the computational limitation associated with numerical models for Dirac-delta function,the source term is expressed as a limiting case of normal distribution.The accuracy of the employed numerical scheme to solve the resulting partial differential equation with appropriate physically relevant boundary conditions is checked with those obtained from the respective analytical solutions available in literature for the particular forms of eddy diffusivity and wind speed.Concentrations computed from the proposed model are found close to those obtained from analytical models.The concentrations obtained from the proposed model are evaluated for the generalized functional forms of eddy diffusivity(Degrazia and Moraes,1992;Degrazia et al.,2001)and diabatic logarithmic profile as well as power-law profile of wind speed with the observations from Hanford(Doran et al.,1984)and Copenhagen(Gryning and Lyck,1984)diffusion experiments in stable and unstable conditions,respectively.Majority of the cases i.e.,64%and 96%are predicted in factor of two to observations in both stable and unstable conditions,respectively.